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Simplifying -16t2 + 35t + 100 = 0 Reorder the terms: 100 + 35t + -16t2 = 0 Solving 100 + 35t + -16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -6.25 + -2.1875t + t2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + -2.1875t + 6.25 + t2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + -2.1875t + t2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + -2.1875t + t2 = 0 + 6.25 -2.1875t + t2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 -2.1875t + t2 = 6.25 The t term is -2.1875t. Take half its coefficient (-1.09375). Square it (1.196289063) and add it to both sides. Add '1.196289063' to each side of the equation. -2.1875t + 1.196289063 + t2 = 6.25 + 1.196289063 Reorder the terms: 1.196289063 + -2.1875t + t2 = 6.25 + 1.196289063 Combine like terms: 6.25 + 1.196289063 = 7.446289063 1.196289063 + -2.1875t + t2 = 7.446289063 Factor a perfect square on the left side: (t + -1.09375)(t + -1.09375) = 7.446289063 Calculate the square root of the right side: 2.728788937 Break this problem into two subproblems by setting (t + -1.09375) equal to 2.728788937 and -2.728788937.Subproblem 1
t + -1.09375 = 2.728788937 Simplifying t + -1.09375 = 2.728788937 Reorder the terms: -1.09375 + t = 2.728788937 Solving -1.09375 + t = 2.728788937 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.09375' to each side of the equation. -1.09375 + 1.09375 + t = 2.728788937 + 1.09375 Combine like terms: -1.09375 + 1.09375 = 0.00000 0.00000 + t = 2.728788937 + 1.09375 t = 2.728788937 + 1.09375 Combine like terms: 2.728788937 + 1.09375 = 3.822538937 t = 3.822538937 Simplifying t = 3.822538937Subproblem 2
t + -1.09375 = -2.728788937 Simplifying t + -1.09375 = -2.728788937 Reorder the terms: -1.09375 + t = -2.728788937 Solving -1.09375 + t = -2.728788937 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.09375' to each side of the equation. -1.09375 + 1.09375 + t = -2.728788937 + 1.09375 Combine like terms: -1.09375 + 1.09375 = 0.00000 0.00000 + t = -2.728788937 + 1.09375 t = -2.728788937 + 1.09375 Combine like terms: -2.728788937 + 1.09375 = -1.635038937 t = -1.635038937 Simplifying t = -1.635038937Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.822538937, -1.635038937}
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